The slope of the tangent to the curve $y = ln\, (cos\,x)$ a $x = \frac{3\pi}{4}$ is
$1$
$-1$
$\ln \,\sqrt 2 $
$\frac{1}{{\sqrt 2 }}$
The side of a square is increasing at the rate of $0.2\,cm / s$. The rate of increase of perimeter w.r.t. time is $...........\,cm / s$
Two particles $A$ and $B$ are moving in $X Y$-plane.
Their positions vary with time $t$ according to relation :
$x_A(t)=3 t, \quad x_B(t)=6$
$y_A(t)=t, \quad y_B(t)=2+3 t^2$
Distance between two particles at $t =1$ is :
If $F = \frac{2}{{\sin \,\theta + \sqrt 3 \,\cos \,\theta }}$, then minimum value of $F$ is